Resonance frequency

1. May 15, 2007

dchen

how can i get the resonance frequency for a damped system?
x'' + 2r x' + w. x = F/m coswt
r is the damping factor, w. the natural frequency

it can be calculated that the amplitude,
A=F/m / sqrt( (w.^2-w^2)^2-(2rw)^2)

by differentiating wrt w,
it is found the maximum amplitude occurs at w=sqrt(w.^2-2r^2)
is this the resonance frequency?

or should i look at the frequency w=sqrt(w.^2-r^2), which is the frequency of the transient solution when the system is not forced.
is the solution at this frequency unbounded?
in the form x=Bt cos (sqrt(w.^2-r^2))t

so which is resonance frequency?
w=sqrt(w.^2-2r^2) or w=sqrt(w.^2-r^2) ??